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Mixture A is 15 percent alcohol, and mixture B is 50 percent

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Mixture A is 15 percent alcohol, and mixture B is 50 percent

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Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0

OA C

Source: Princeton Review

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BTGmoderatorDC wrote:
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0
A = 15% alcohol
B = 50% alcohol
The MIXTURE of A and B = 30% alcohol

To determine the ratio of A to B, use ALLIGATION -- a very efficient way to handle mixture problems.

Step 1: Plot the 3 percentages on a number line, with the percentages for A and B (15% and 50%) on the ends and the percentage for the mixture (30%) in the middle.
A 15-----------30------------50 B

Step 2: Calculate the distances between the percentages.
A 15----15----30----20----50 B

Step 3: Determine the ratio in the mixture.
The ratio of A to B is equal to the RECIPROCAL of the distances in red.
A:B = 20:15 = 4:3.

Of every 7 pounds, 4 pounds = A and 3 pounds = B, implying that A constitutes 4/7 of the 4 gallons:
(4/7)(4) = 16/7 ≈ 2.3

The correct answer is C.

Other alligation problems:
http://www.beatthegmat.com/mixture-problem-rabbit-proteins-t190121.html#593241

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